Stephen Lucas Salters Horners A2 Physics Coursework What affects the range of a trebuchet? By Stephen Luca s 1 Stephen Lucas Salters Horners A2 Physics Coursework What affects the range of a Trebuchet? Planning Aim: To find which factors limit the distance travelled by a projectile fired from a small scale tabletop trebuchet, and therefore to find which conditions are necessary for optimum range. Hypothesis I anticipate that the greatest range of the trebuchet will be achieved when there is: A large ratio of counterweight mass to projectile mass – i.e. the mass of the counterweight is far greater than the mass of projectile. A large distance between the fulcrum and the projectile. A large height above the ground from which the counterweight is suspended. The use of aerodynamic projectiles. Minimum friction about the fulcrum. The use of a light swing arm. Introduction A trebuchet is a siege engine that was predominantly employed in the middle ages to smash masonry walls and to hurl objects such as diseased bodies into the castle grounds to infect the inhabitants under siege. Although trebuchets are no longer used in modern warfare due to technological advances, some are still in existence for medieval reconstructions, such as the fire ball throwing trebuchet at Warwick Castle. Figures 1 & 2 – The trebuchet in use at Warwick Castle: The range of the trebuchet would have been a vital piece of information both to the armies using them at the time and to those trying to reconstruct one for entertainment. A large range would have enabled the armies using them to attack castles without being in range of the enemy archers and so producing vast amounts of damage with few casualties of their own. If the range of the trebuchet was too small then the armies using them would be vulnerable, and those trying to recreate the medieval experience at historical attractions would lose the interest of an audience. 2 Stephen Lucas Salters Horners A2 Physics Coursework Knowing the velocity of the projectile as it leaves the swing arm of the trebuchet would have also been a crucial piece of information for those controlling them, since this could be used to accurately predict the maximum height reached by the projectile (i.e. will it get over the castle wall) and where the projectile will land, and thus with what velocity will it strike the target at (determining the potential damage it could cause). The trebuchet I shall be constructing is designed to operate safely within a classroom so it will be relatively small and designed to hold reasonably light weights, giving a measurable distance of the range of the projectile. In order to deduce the factors that affect the range of the trebuchet, I will be keeping the mass of the projectile constant while using increasing masses of counterweights. I will also be using varying masses for projectiles while keeping the mass of the counterweight constant and then collectively looking at these results to see which ratio of counterweight mass to projectile mass gives the maximum range. The trebuchet arm is also drilled with three different holes, each drilled increasingly further from the end that the counterweight is suspended from. These three holes correspond to three different distances between the fulcrum and counterweight and projectile, giving three different heights above the ground level from which the counterweight will be held. By looking at these three variables individually, it should be clear as to which factors produce the greatest range. Construction of the Trebuchet The materials used will have to be easily obtainable, and for this reason I shall be constructing the frame of the trebuchet from MDF and the swing arm from pine wood. The arm must be able to be drilled and hammered without cracks spreading and to support weights that have more mass than itself. Pine is suitable for this purpose as it is strong and stiff, and so will not deform when the counterweight is added and will require a large force before the arm breaks. Pine has an approximate Young Modulus of: 5.49 x 109 Pa. The MDF is not of high quality, however its purpose in terms of the trebuchet is to provide support and so it will not experience a great deal of weight or impact and so serves this purpose well. The MDF will be connected via super glue using a glue gun and small nails where necessary to increase its strength as a base. The fulcrum will consist of a brass wire with a constant diameter of 2.9 x 10-3m, this diameter closely matches the diameter of the holes produced by the drill, and its smooth surface will offer negligible friction to the swinging motion of the arm. The fact that the diameter closely matches the holes drilled will allow the arm to complete its circular arc without wobbling. The metal wire is light and stiff, so it will not bend as masses are added to the trebuchet or exert a great deal of force on the base. The following apparatus was utilised for the construction of the trebuchet: * MDF (one inch by one half inch thick): - 12 inch length x 2 - 10 inch length x 2 - 5 inch length x 3 3 Stephen Lucas Salters Horners A2 Physics Coursework - Square piece of flat wood ( 6 inches by 6 inches) * Pine (Cross-sectional area of: 2.28 x 10-4m2): - 16 inch length x 1 * Glue gun with glue sticks * Eyehooks x 2 * Small screws * Small nails * Hammer * Drill *Tape measure and ruler Great care was taken when constructing the trebuchet to ensure that the trebuchet was constructed safely, and that holes were drilled in straight lines and at central points where necessary. The use of machinery to cut the wood was performed by experienced technology teachers. Changes made to the initial design of the trebuchet after testing The original design of the trebuchet was to have a fabric pouch in which the projectile would be stored. This pouch would be stored underneath the swing arm and swing outwards as the counterweight fell to the ground. Each end of the fabric pouch would have a piece of string coming off of it, which would be connected to one end of the trebuchet arm. One of the pieces of string would be firmly tied around the eye hook at the end of the trebuchet arm. At the end of the other string would be a metallic ring that would slot onto a hook at the same end of the trebuchet arm. As the trebuchet arm swung forward, the metallic ring would slide off the hook, releasing one of the strings, opening up the pouch and hurling the projectile forward. Figures 3 & 4 – The original design of the trebuchet with the string and pouch: After constructing this type of trebuchet, it proved to be unsuccessful in producing enough data to be harvested. The pouch that stored the projectile resisted releasing it as the edges of the pouch did not allow free movement. The metal ring resting on the hook also did not consistently fall off the hook, meaning that the projectile remained in the pouch or did not travel any notable distance on many attempts. In addition the background physics behind this type of trebuchet involved differentials and appeared to be too complicated for this level. The trebuchet was then modified so that the projectile was fired every time and could easily be analysed. The fabric pouch was replaced with a plastic spoon super-glued to the top of the trebuchet arm. At the end of the plastic spoon, blu-tack was stuck to form a vertical barrier, so that the projectile was securely held and could not fall free before being released. This type of trebuchet produced consistent launches and very rarely failed to launch the projectile. 4 Stephen Lucas Salters Horners A2 Physics Coursework Figure 5 – Side view of the final trebuchet: Eye hook supporting counterweight (string is thread through the eye hook and around the counterweight) Fulcrum Base of Trebuchet The end of the swing arm to which the spoon is attached Spoon – where projectile is held Trebuchet Arm Fulcrum (There is Blu-tack at each end to keep the fulcrum in place) Counterweight Trebuchet Base Figure 6 – Front view of the trebuchet. Information on the final design of the Trebuchet Mass of Trebuchet (kg) 4.9715 x 10-1 Mass of Arm (kg) 6.205 x 10-2 Mass of Base (kg) 4.351 x 10-1 Distances from the counterweight hook to 0.076 0.103 0.128 the fulcrum (m) Distances from the projectile holder to the 0.412 0.386 0.360 fulcrum (m) Maximum height of Counterweight from 0.276 0.295 0.335 ground level (m) *without string Height of projectile before release (m) 0.670 0.647 0.624 Angle made with ground and the projectile 0.681 0.801 0.855 holder before release (radians) * Rounded to 3 decimal places The previous table is the table referred to when making calculations and trying to anticipate how far the projectile will travel and with what velocity it will be released. 5 Stephen Lucas Salters Horners A2 Physics Coursework Projectile Motion The distance travelled by a projectile can be calculated by resolving the vertical and horizontal components of the projectile’s initial velocity. The two vertical and horizontal components of the motion are independent of each other and so can be treated separately. For simplicity I will assume that air resistance is negligible, so that the only force acting on the projectile after it leaves the swing arm of the trebuchet is gravity.